code: def __init__(
      self,
      stat: float,
      pvalue: float,
      crit_vals: pd.Series,
      null: str = "No Cointegration",
      alternative: str = "Cointegration",
      trend: str = "c",
      order: int = 2,
      xsection: RegressionResults | None = None,
      test_type: str = "Za",
      kernel_est: lrcov.CovarianceEstimator | None = None,
      rho: float = 0.0,
  ) -> None:
      super().__init__(
          stat,
          pvalue,
          crit_vals,
          null,
          alternative,
          trend,
          order,
          xsection=xsection,
      )
      self.name = f"Phillips-Ouliaris {test_type} Cointegration Test"
      self._test_type = test_type
      assert kernel_est is not None
      self._kernel_est = kernel_est
      self._rho = rho
      self._additional_info.update(
          {
              "Kernel": self.kernel,
              "Bandwidth": str_format(kernel_est.bandwidth),
              "Trend": self.trend,
              "Distribution Order": self.distribution_order,
          }
      )
  
imports: from __future__ import annotations
  from typing import cast
  import numpy
  import pandas
  from scipy import stats
  from statsmodels.iolib.summary import Summary
  from statsmodels.iolib.table import SimpleTable
  from statsmodels.regression.linear_model import RegressionResults
  import arch.covariance.kernel
  from arch.typing import ArrayLike1D, ArrayLike2D, Literal, UnitRootTrend
  from arch.unitroot._shared import KERNEL_ERR, KERNEL_ESTIMATORS, ResidualCointegrationTestResult, _cross_section
  from arch.unitroot.critical_values.phillips_ouliaris import CV_PARAMETERS, CV_TAU_MIN, PVAL_LARGE_P, PVAL_SMALL_P, PVAL_TAU_MAX, PVAL_TAU_MIN, PVAL_TAU_STAR
  from arch.unitroot.unitroot import TREND_DESCRIPTION
  from arch.utility.array import ensure2d
  from arch.utility.io import str_format
  from arch.utility.timeseries import add_trend
label_desc: Use image node_id 1 to create a new PhillipsOuliarisTestResults object from inherited base classes: ResidualCointegrationTestResult with example: obj = PhillipsOuliarisTestResults(stat, pvalue, crit_vals, null, alternative, trend, order, xsection, test_type, kernel_est, rho)